The present invention relates generally to the field of image reconstruction in computed tomography (CT) systems and, more particularly, to a method and apparatus for rebinning cone beam projection data into a series of two-dimensional sinograms based on an optimized ray consistency approach.
Computed tomography (CT) imaging systems operate by projecting fan shaped or cone shaped X-ray beams through an object. The X-ray beams are generated by an X-ray source, and are generally collimated prior to passing through the object being scanned. The attenuated beams are then detected by a set of detector elements. The detector elements produce a signal based on the intensity of the attenuated X-ray beams, and the signals are processed to produce projections. By using reconstruction techniques, such as filtered backprojection, useful images are formed from these projections.
A computer is able to process and reconstruct images of the portions of the object responsible for the radiation attenuation. As will be appreciated by those skilled in the art, these images are computed by processing a series of angularly displaced projection images. This data is then reconstructed to produce the reconstructed image, which is typically displayed on a display monitor, and may then be printed or reproduced on film or further processed by other software, such as computer aided detection software. When performing a CT scan where a cone-beam of x-rays is projected toward an object, special challenges are introduced into image reconstruction. That is, 3D image reconstruction of cone-beam projections poses significant challenges in regards to reconstruction algorithms that accurately and efficiently produce a CT image. This holds true, in particular, for a helical scan geometry, where the x-ray source moves along a segment of a helix relative to the object.
Previously, several algorithms have been developed to reconstruct cone beam data. One such algorithm is the Feldkamp algorithm, which is an approximate reconstruction algorithm for helical cone beam CT. The Feldkamp algorithm is a 3D filtered backprojection (FBP) algorithm in which a 1D row-by-row filtering of each projection and cone beam backprojection is performed, using either a full-scan or a short-scan set of data to reconstruct transaxial slices. This cone beam backprojection leads to numerical inefficiency in the reconstruction of the FDK algorithm.
Another algorithm that has been developed to reconstruct cone beam data is the PHI algorithm. The PHI algorithm is an exact/quasi-exact algorithm that yields accurate reconstructions by discretizing exact analytical inversion formulae for a 3D divergent-beam x-ray transform. This exact or quasi-exact algorithm yields accurate reconstructions even for very large values of the cone-angle. However, it involves complex data processing compared to two-dimensional (2D) reconstruction approaches and this complexity increases the reconstruction time by more than one order of magnitude. Thus, while accurate, the PHI algorithm is slow and numerically complex.
In order to decrease reconstruction time for helical cone-beam CT over the above mentioned techniques, and other similar techniques, rebinning is often used to convert cone beam data into a series of approximate 2D sinograms. This allows for the reconstruction of a plurality of 2D sinograms, which is less computationally intensive than 3D reconstruction, and is thus much more efficient. One drawback to current rebinning methods, however, is that most of the rays needed in the 2D sinograms are not actually measured. Rather, the majority of the rays used in the sinograms are approximated using the available data received from the cone beam. This approximation introduces errors that can result in significant errors in the final reconstructed image.
In the case of reconstructing data obtained in a helical cone-beam CT scan by way of 2D reconstruction algorithms, a set of 2D sinograms is generated from the cone beam data. If 2D parallel beam reconstruction is used, cone beam data is rebinned from a cone beam to a cone-parallel geometry. After this rebinning, the data is described by the function g(β,s,γ), where β is the (parallel) view angle, s denotes the signed distance between the rotation axis and the ray, and γ is the cone angle of the ray. Note that the variable β increases by 2π for each rotation of the helix—it does not, for example, wrap back around to zero after each rotation. This data can be rebinned to 2D parallel data at a series of z locations (zn) as follows:p(θ,s,zn)=wr(ζ1,s)g(βn+ζ1,s,γ(ζ1,s))+wr(ζ2,−s)g(βn+ζ2,−s,γ(ζ2,−s))  [Eqn. A],with ζ1=mod(θ−βn+π, 2π)−π and ζ2=mod(θ−βn,2π)−π, and βn being the parallel view angle associated with zn, and where γ(ζ,s) is a cone angle that covers a domain of ζ from −π to π and s, from −Ro to Ro, where Ro is the radius of the field of view, and where wr(ζ,s) is a redundancy weight that covers the same domain and has the property that wr(ζ,s)+wr(ζ+π,−s)=1 when ζ<0. Also, p(θ,s,z) is computed over a domain of θ from 0 to π and s from −Ro to Ro.
In one previously known technique, wr(ζ,s)=1 for |ζ|<π/2. This implies wr is equal to zero elsewhere. Additionally, for the function γ, the value of the function is set such that:tan(γ)=(zn−zs)/(2*√{square root over (R2−s2))}  [Eqn. B],
where zs is the z location of the source when the rays g(βn+ζ,s) are measured. This choice of the function γ corresponds to a traditional helical interpolation and leads to an approximation of the 2D sinogram for an axial slice of an image volume. While computationally more efficient than 3D reconstruction algorithms, a drawback to this technique is that the approximation error present in approximating the 2D sinograms is very high. As such, a loss of resolution occurs in the final reconstructed image.
In another known technique set forth in U.S. Pat. No. 5,802,134 to Larson et al., planar axial slices (i.e., image slices) in the imaging volume are defined such that they define a tilt angle and a rotation angle with respect to a rotation axis (i.e., the z axis or longitudinal axis). Successive planar slices have equal tilt angles but changing rotation angles such that normal axes of successive slices define a nutation and precession about the rotation axis. That is, the function γ(ζ,s) is chosen such that rays in the cone beam are as consistent as possible with the pre-selected planar slice. Thus, by attempting to select rays most consistent with a pre-defined plane, a plurality of the rays used in reconstructing the 2D sinograms for the planar image slices are still approximated, which can lead to errors in the final reconstructed image.
Therefore, it would be desirable to design an improved apparatus and method that generates a plurality of 2D sinograms to reduce the reconstruction time for helical cone beam data. It is also desirable to design an apparatus and method for rebinning cone beam data that reduces the error associated with the rebinning process.